经典可实现的不相容性
Classically Realizable Incompatibility
浏览论文内容
中文总结 AI 辅助
研究量子力学中不相容性场景，在部分布尔代数框架下，引入通过经典博弈实现不相容性场景的统一方法，证明排他图是嵌入布尔代数的排他pBA的原子图，给出排他图必要条件和原子图充分条件。
中文摘要 AI 辅助
不相容性是量子力学的一个基本方面。然而，并非每个量子可观测量的非经典性质都源于不相容性，也并非所有量子场景都能仅通过不相容性完全捕捉。在部分布尔代数（pBA）框架内，我们研究不相容性场景的结构性质。我们引入一种通过经典博弈实现任何不相容性场景的统一方法，该构造可扩展到任何可嵌入布尔代数的场景。排他图提供了不相容性场景的精确表征。我们证明每个排他图都是嵌入布尔代数的排他pBA的原子图。这些结果为排他图提供了必要条件，为原子图提供了充分条件。
英文摘要
Incompatibility constitutes a fundamental aspect of quantum mechanics. However, not every quantum observable non-classical property arises from incompatibility, nor can all quantum scenarios be fully captured by incompatibility alone. Within the framework of partial Boolean algebra (pBA), we research the structural properties of incompatibility scenarios. We introduce a unified method to realize any incompatibility scenario via a classical game, and the construction is extendable to any scenario embeddable into a Boolean algebra. The exclusivity graph offers a precise characterization of incompatibility scenarios. We prove that every exclusivity graph is the atom graph of an exclusive pBA, which is embedded into a Boolean algebra. These results provide a necessary condition for exclusivity graphs and a sufficient condition for atom graphs.
